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Elizabeth Warren, whose potential Senate candidacy has piqued national interest, began a “listening tour’’ this week, convening a set of invitation-only events where she has shown her fiery side to small groups of friendly Democratic activists desperate to defeat Republican Scott Brown.

Those in attendance at a Dorchester home Monday night said she sprinkled her answers with punchy words about her time in Washington, where she fought for legislation creating a consumer protection bureau for President Obama in the aftermath of the banking crisis.

“She either wanted to get the bill as it was written or she wanted to leave with no bill but with ‘blood and teeth on the floor,’ ’’ said Joyce Linehan, a Dorchester activist who hosted the event at her home, where about 60 people shared Italian sandwiches and beer. “And for some reason, my friends have glommed onto that one [line] like no other.’’

Warren, a Harvard law professor who has never run for political office, has told crowds that she has not made up her mind.

But the listening-tour strategy, common for many first-time politicians and popularized by Hillary Rodham Clinton when she ran for Senate in New York, allows candidates to test-market talking points and familiarize themselves with retail politics before submitting to the full glare of the campaign spotlight.

At the same time, Warren can build enthusiasm among the most passionate members of her party, many of whom have expressed dissatisfaction with the current field of six announced candidates.

Warren also made a stop on Monday at a private home in her hometown, Cambridge, and in Arlington yesterday. Later this week, she plans to visit homes in Framingham, Shrewsbury, New Bedford, Falmouth, Brockton, Springfield, and Pittsfield, according to a Democratic operative. Other locations may be added.

The events are being organized hastily by Doug Rubin and Kyle Sullivan, consultants who helped orchestrate Governor Deval Patrick’s two campaigns.

Warren has yet to speak to any Massachusetts-based reporters or hold any events for the general public, sparing her exposure to potentially confrontational audiences. She has not published the locations of the events, but several have leaked out from attendees who have posted photos and gushed on Twitter. Between the meetings, she is calling high-level Democrats in the state, including Patrick.

Several of those who attended the events said Warren sought to allay Democrats’ fears that she would run a dispassionate campaign, like the one many believe fellow Democrat Martha Coakley waged against Brown in last year’s special election.

“She really had thought about it . . . what had gone wrong the last time and what would be required for her to run,’’ Jen Deaderick, a Cambridge writer who runs an Equal Rights Amendment page on Facebook, said of Warren.

Stephanie J. Anderson, an Ashmont resident, said, “My question for her was simply: Do you have what it takes? We know that you’re right on the issues. We know about your intellectual horsepower, but do you have what it takes to get out there and hustle and not be outworked? Because I’m a loyal Democrat, but I believe Scott Brown won that seat.’’

Warren, she said, responded by talking about her unemployed family members in the construction industry and her own experience growing up on “the jagged edge of the middle class.’’

“It was a lengthy answer,’’ said Anderson, who managed Tito Jackson’s initial unsuccessful campaign for Boston City Council in 2009. “I’m sure her answers will become much more concise as she becomes a well-honed candidate.’’

Brown and the Republican Party have begun targeting Warren directly in fund-raising appeals and public statements. Yesterday, Brown posted a letter on his Web page asking supporters to counter the $100,000 raised by a Washington-based group, Progressive Change Campaign Committee, that is trying to draft Warren. Calling her a “liberal professor,’’ Brown’s fund-raising letter said Warren shares the group’s “far left-wing agenda for America: higher taxes, bigger government, and more spending.’’

Democrats, the letter continues, are “so obsessed with winning this seat back that Washington elitists are trying to push aside local Democrat candidates in favor of Professor Warren from Oklahoma.’’

Those who attended the Warren meetings say they believe she can combat those attacks with a full-throated defense of middle-class values. She has mentioned Brown only glancingly.

“She said he was handsome; that was just a joke kind of thing,’’ said Jimmy Cawley, a human services worker who lives in Hyde Park. “She said he was probably a very, very nice guy, but our political ideas are very different.’’

Cawley said some in the crowd complained about Obama, saying they were disappointed in his performance after all the work they had put in to elect him. Warren blamed the partisan atmosphere in Washington and implored the activists to work on issues rather than assign blame, he said. Cawley, who has worked on several campaigns, said he believes Warren will probably enter the race and would be the only Democrat capable of defeating Brown.

“Realistically, politically, I don’t think any of the current contenders can beat him,’’ he said. “I don’t think they have the juice to take Scott out.’’